computational investigation of cavity flow control using a passive device

7/30/2019 Computational investigation of cavity flow control using a passive device

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Computational investigation of cavity flow control usinga passive device

B. Khanal, K. Knowles and A. J. Saddington

Cranfield UniversityDefence Academy of the United Kingdom

Shrivenham, SN6 8LA, England

Abstract

In this paper, flow control effectiveness of a passive device in relation to open cavityflowfield is investigated computationally and compared with experimental work. Specific-ally the modification in the cavity flowfield due to the presence of a spoiler is studied indetails to explain the physics behind the flow control effects. A combination of 2D and 3Dflow visualization tools are used to understand the flow behaviour inside the cavity and thequantitative analysis of the unsteady pressure fluctuations is also performed to assess theunsteady effects. Flow simulations with a turbulence model based on a hybrid RANS/LES(commonly known as Detached-Eddy Simulation [DES]) are used in this study. The time-mean flow visualization clearly showed the presence of three dimensional effects inside theempty cavity whereas the 3D effects were found to diminish in the presence of a spoiler. Inthe unsteady flow analysis, near-field acoustic spectra were computed for empty cavity as

well as cavity-with-spoiler cases. Study of unsteady pressure spectra for the cavity-with-spoiler case was found to record the complete suppression of the dominant tones in thepresence of the spoiler. The analysis has indicated that the main reason behind this sup-pression is due to the inability of faintly energized vortical structures (faintly energized as aresult of the extraction of turbulent kinetic energy by the spoiler) to maintain the unsteadyflapping of the separated shear layer.

PhD Research studentProfessor and Head of Aeromechanical Systems GroupLecturer; Aeromechanical Systems Group

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Computational investigation of cavity flow control using a passive device

Nomenclature

2D Two-dimensional3D Three-dimensionalCFD Computational fluid dynamicsCp Pressure CoefficientD Cavity depth, mfn frequency of the nth mode, HzK ratio of the velocity in the shear layer to the freestream velocity

L Cavity length, mLIC Line Integral Convolution

M Flow Mach numbern Cavity oscillation mode numberSt Strouhal number, St= f D/UU Freestream velocity, m/sW Cavity width, mx,y,z Cartesian coordinate system, origin at the top left corner of the upstream wall an empirical constant, = 0.062(L/D) Boundary layer thickness at a velocity of 0.99U, m fluid density, kg/m3

Ratio of specific heats of test fluid (= 1.4 for air)

1 Introduction

Cavity geometries are frequently encountered in aerospace applications, such as wheel wells,

weapons bays, and other fuselage openings and are also widely known to be the major contrib-utor of aerodynamic noise. Unsteady flow approaching a simple cavity geometry produces com-plex features consisting of flow-induced resonant tones, multiple flow and acoustic instabilities,and wave interactions. Cavities do also have some benefits, particularly, the internal weaponsbays on military aircraft have several design advantages. Reduced aerodynamic drag, low radarcross-section and avoidance of aerodynamic heating of the store are a few examples of these.However, once the weapons bay doors are opened, the flowfield is dependent on the cavity geo-metry and the freestream flow conditions. The resultant unsteady flowfield undergoes interactionwith the stores at the beginning of the store release leading to several undesirable aerodynamiceffects. The self-sustaining pressure fluctuations in the cavity can cause cavity resonance whichin turn leads to structural fatigue of the aircraft and the store. In addition, the interaction of the

store with the unsteady shear layer formed over the cavity can lead to unpredicted motion of thestore. Hence, a study of cavity flowfield is necessary to understand the flow physics responsiblefor these phenomena and to propose a suitable methods to control them.

Numerous studies [1, 2, 3] have been carried out to understand complex flow features ex-isting in cavities and many more [4, 5, 6] are continuing to understand the cause behind suchcomplex flowfields and suppressing the resonant tones. Although initially the suppressing tech-nique might seem simple enough such that any scheme that disrupts the resonance mechanismcan be used to suppress resonant tones, finding a practical solution is not straightforward. Thereare currently three main approaches which are being used to vary the way the flow behaves inthe cavity. They are: passive, active open-loop, and closed-loop flow controls. Passive methodsinvolve manipulating the cavity geometry by either modifying the cavity walls slanting angle

or adding mechanical devices to deliberately alter the flow inside the cavity. The other two

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methods involve manipulating the flow inside the cavity by devices that require external energyinput e.g. jets or oscillating flaps. They can be either of the open- or closed-loop types. Closed-loop control requires the implementation of a feedback loop in the control system allowing it to

continuously monitor and update the control parameters to match the changing flow conditions.Hence, closed-loop control systems are more suitable for time-varying and off-design situations.The closed loop system developed by [7] to suppress the resonant modes from a weapons-baywas not very successful although this was blamed on the poor performance of the actuators.Active open-loop methods have been found to be limited by actuator bandwidth, and they re-quire large actuator power to be effective [7] whereas closed-loop techniques introduce greatercomplexity and are not mature enough yet. At this point, it is important to point out that passiveand active open-loop schemes break the resonance cycle in a fundamentally different way tothe closed-loop counterparts. Because the dynamics of a linear system cannot be changed withopen-loop control, any open-loop method used to modify the cavity resonance cycles must doso at finite amplitudes, typically at amplitudes comparable to the tones being suppressed. By

contrast, closed-loop control can act by changing the dynamics of the linear system, which im-plies that low-power actuators can be used effectively. A classification of various flow controlscheme is depicted in Fig 1 [8]. In this work, computational study of empty cavity and cavity inpresence of passive devices (spoiler in this case) are performed using a turbulence model basedon one-equation DES formulation [9].

Figure 1: Classification of flow control methods, from [8].

With regards to the choice of turbulence model selected in this simulation, it is necessaryto highlight the limitations of Reynolds-averaged Navier-Stokes (RANS) solver. Several com-putational studies in the past have experienced a common limitation with RANS solver andturbulence models applied to unsteady flows [9, 10, 11]. The RANS solver produces increasededdy viscosity which causes excessive damping of the unsteadiness of the flowfield. Spatiallyfiltered models such as Large-Eddy Simulation (LES) have provided improved results for sim-ulating unsteady flows. LES models, however, are currently limited to low Reynolds numbers

because of the computing resources required to resolve the small-scale turbulent structures. LES

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is not yet, therefore, a feasible tool for the simulation of cavity flowfields at transonic speeds.Recently, hybrid methods which behave as a standard RANS model within the attached bound-ary layer and as a LES Sub-Grid Scale model in the rest of the flow (more commonly known as

DES) have been introduced to address this problem [9, 12, 13]. A hybrid RANS/LES model [9]was, therefore, chosen for this study.

Cavity flows are usually classified by the length-to-depth ratio (L/D) of the cavity and fourdifferent types of cavity flows are found to be present depending on the value of this ratio. Theexperimental study of Stallings and Wilcox [14] in the 1980s led to the classification of thecavity flow types. Schematics representing all four cavity flow types and corresponding floorpressure distributions are shown in Figure 2.

Cavity flows exhibit a wide variety of phenomena whose precise nature depends sensitivelyon a number of parameters including the value ofL/D. Tracy and Plentovich [16] investigatedthe variations in the values ofL/D and concluded that the dependence of the cavity flow type onMach number in addition to L/D. The other important parameters that affect cavity flow types

are incoming boundary layer thickness (), ambient density (), viscosity (), and speed ofsound (a0). Although the underlying physical mechanisms vary, it is known that self-sustainingoscillations develop over a wide range of these parameters. In compressible flows, cavity oscil-lations are typically described as a flow-acoustic resonance mechanism. This mechanism maybe summarized as follows: small instabilities in the shear layer interact with the downstreamedge of the cavity and generate acoustic waves. These acoustic waves propagate upstream tothe region near shear layer separation where they induce localized instabilities, thereby closingthe feedback loop. This type of instability is referred to as a shear-layer (or more commonlyRossiter) mode, attributed to the early experimental work of Rossiter [17]. This led to the de-velopment of a well-known semi-empirical formula which can be used to predict a given modefrequency of oscillation for a given cavity geometry:

fn =U

L

n

M+1K

(1)

where fn is the frequency corresponding to the nth mode, M is the freestream Mach number,K is the ratio of disturbance velocity in the shear layer to the freestream velocity, (a value ofK= 0.57 is widely used; although this value is appropriate for thin initial boundary layers, itdecreases with increasing boundary layer thickness.) and is an empirical constant employedto account for the phase lag between the passage of a vortical disturbance past the cavity trailingedge and the formation of an upstream travelling disturbance. The value of depends on L/D

and is evaluated as : = 0.062(L/D). Rossiters model is generally found to agree well withexperimental results at moderate subsonic Mach numbers. At transonic and supersonic Machnumbers temperature recovery within the cavity is important and hence it is essential to accountfor the increased sound speed within the cavity [18]. To accommodate these high Mach numberranges, Eq. 1 was subsequently modified to predict the frequencies of the various oscillationmodes as follows:

fn =U

L

n

M 1+(1)

2 M2

12+ 1

K

(2)

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Dividing

streamline

Separation point Stagnation point

(a) Open cavity flow.

(b) Transitional-open cavity flow. (c) Transitional-closed cavity flow.

Dividing streamline

Stagnation pointSeparation point

Impingement point Separation point

(d) Closed cavity flow.

+

0

0 1

Cp

x/L

+

0

0 1

Cp

x/L

+

0

0 1

Cp

x/L

+

0

0 1

Cp

x/L

+

0

0 1

Cp

x/L

+

0

0 1

Cp

x/L

(a)

(b) (c)

(d)

TransitionalOpen Closed

L/D increasing

(e) Cavity flow type classification, based on floor pressure distributions.

Figure 2: Cavity flow types and corresponding pressure distributions [15].

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where is the ratio of specific heat of the test fluid (= 1.4 for air). The CFD results presentedin this paper use Eq. 2, also known as "modified Rossiter Equation", to predict the frequenciesof the various oscillation modes in cavities. This work is continuation of our effort [19] on

understanding the open cavity flow behaviours and, exploring practical and effective methods tosuppress the resonant modes.

2 Computational Solver

The commercial CFD solver FLUENT was used to simulate all the cavity cases consideredin this paper. FLUENT is a finite-volume solver and the temporal and spatial discretizationschemes available in it provide at most second-order accuracy in space and time. Options forboth explicit as well as the implicit time-stepping are available with the solver. The implicittime-stepping option was used on all the simulated results presented in this paper. To modelthe turbulent unsteady flowfield inside the cavity, Detached-Eddy Simulation (DES) based ona one-equation model [20] was used. DES is a hybrid model which behaves as a standard SARANS model within the attached boundary layer and as a Large-Eddy Simulation (LES) Sub-Grid Scale (SGS) model in the rest of the flow. The standard RANS SA turbulence model[20] uses the distance to the nearest wall to define a length scale d that is used to calculate theproduction and the dissipation terms of turbulent viscosity. In the DES formulation of the SAturbulence model [9], the length scale d is replaced with a DES length scale dDES defined as:

dDES = min(d,CDES) (3)

= max(x,y,z) (4)

where CDES is a constant with a value of 0.65 for the DES model and is the largest celldimension in the computational grid. The modified length scale calculated using the relationsin Eq. 3 ensures a length scale that is the same as the standard SA RANS value near the wallswhere d> . Theeffect of this is to activate a hybrid SA turbulence model that behaves as a standard SA RANSmodel within the attached boundary layers and as a LES Sub-Grid Scale model in the rest ofthe flow including the separated regions. From Eq. 3, it can clearly be seen that this model isgrid-dependent and, hence, any solution using it also relies on the grid design, i.e. dependingon whether the cells in the attached boundary layer are carefully designed, a local grid spacingas the length scale will be activated rather than the standard SA RANS length scale required inthe boundary layer.

3 Geometry and Flow Setup

Two types of cavity geometries were considered in this investigation. Both the cavity were10cm long with an L/D of 4 and W/D of 2.4 (see also Figure 3) and had identical flow andgeometrical settings to the experimental studies of Geraldes [21]. The first type is a three-dimensional plane cavity, which comprises a simple rectangular cutout in an otherwise infiniteplate. The second type had exactly the same basic cavity dimensions as the first, the onlydifference being the presence of serrated spoilers immediately upstream of the cavity leadingedge. The spoiler geometry is a slightly modified version of the coarsest (also termed as large

spoiler) sawtooth spoiler used by Geraldes [21] and therefore it had identical flow conditions

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to the experiment. Each of the triangular elements in the experiment measured 7.375mm wideand 3.6875mm high. In this study, the spoiler geometry was modified to facilitate good qualitystructured grid generation in the upstream boundary layer where spoilers are located. To resolve

the boundary layer correctly, structured grid cells with low skewness angles are essential andthis is crucial for accurate prediction of the flowfield inside the cavity. To ensure the consistencywith the experiment, the sawtooth profile was modelled as a trapezium of identical heights andsurface area. The only variables were then the width of the top and the bottom parallel sideswhich were chosen to be 2.95mm wide and 4.425mm respectively. The spoiler profiles areshown in Figure 4.

(a)Clean Cavity.

(b)Cavity with Spoiler.

Figure 3: Isometric views of the clean cavity and cavity with spoiler.

The 3D computational domains for both the cases were generated using structured meshingstrategy. The non-matching grid interfacing techniques were utilized in both the computed casesto minimize the number of grids in the structured domains. The extent of the three-dimensionalcomputational domain and mesh density were chosen following preliminary two-dimensionalnumerical simulations. Due to the excessive computational time involved in 3D unsteady com-putations, two-dimensional simulations were used to establish grid convergence. For this pur-pose three meshes were generated with the same basic mesh topology, but with varying griddensities. In this way, an optimum 2D grid was established. The 2D grid was chosen as the

basis for the 3D grid generation. The 3D computational domain extended 4L upstream, 5L

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(a) Experiment.

(b) CFD.

Figure 4: Spoiler geometry.

downstream and 3L vertically and laterally from the cavity walls. For the DES simulation,the 3D grid cells are ideally required to be isotropic. Hence both the cavity meshes had nearisotropic cells inside the cavity with minimum stretching. Figures 5 and 6 show the sectional

views of the three-dimensional computational domain for the first case (similarly, Figures 7 and8 for the second case). The grid cells inside the cavity were maintained close to cubic volumeswith a minimum amount of stretching (evident from the zoomed views in the figures) so thatan LES-type length scale is invoked inside the cavity. In total, the computational domain con-sisted of approximately 2.6 million structured grid points for the first case (2 .79 million for thesecond case). Along the inflow boundary, the two Cartesian velocity components u, v were pre-scribed so that the computed boundary layer just upstream of the cavity had approximately thesame thickness as in the experiment [21]. The boundary layer thickness near the cavity leadingedge in the experiment was approximately 0.015m whereas with the specification of the profileupstream, the boundary layer thickness achieved in the CFD near the cavity leading edge was0.0101m. All the solid surfaces (cavity walls and flat plates) were treated as adiabatic walls with

a no-slip condition. The rest of the boundary faces were set as pressure farfield. The lateralextents (side face) of the computational domain were at 3L from the cavity side walls so thatthe solution inside and around the cavity was not affected by the choice of the pressure far-field boundary conditions (Author had also tested another combination of boundary conditions(a combination of the pressure outlet, outflow and symmetry/periodic on the side faces of thedomain; which showed very little effect on the flow inside the cavity compared to the pressurefarfield boundary). In addition, the use of pressure farfield improved the stability of the solver(In the authors experience, the pressure farfield boundary helps the stability while using densitybased solvers).

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(a) Section view of grid in empty cavity.

(b) Section view of grid (zoomed in).

Figure 5: Structured grid distribution across XY-plane.



Figure 6: Structured grid distribution across XZ-plane.

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Figure 7: Structured grid distribution across XY-plane.

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Figure 8: Structured grid distribution across XZ-plane.

4 Computed Results

The CFD solver FLUENT was used to simulate both the cavity cases considered in this pa-per. FLUENT is a finite-volume solver and the temporal and spatial discretization schemesavailable in it provide at most second-order accuracy in space and time. Many studies [22, 23]have shown FLUENT to be capable of simulating unsteady flow problems, and of resolvingthe flow structures responsible for noise generation when suitably designed computational meshand time-step sizes are used. Options for both explicit as well as the implicit time-stepping areavailable with the solver. The spacial discretization used in the simulations was flux differencesplitting based on second order upwind (default option for compressible flow in Fluent) with asecond order central differencing applied to the modified turbulent viscosity and a second orderimplicit scheme was adopted for temporal discretization. Due to the transonic speed involved,a coupled solver was chosen to ensure a fully compressible solution and a constant time step(constant time-stepping is essential for the time consistency of the resolved unsteady structuresespecially in DES simulations) of 1105s (approx. 2.9% ofL/U) was maintained for theunsteady simulation. The simulations were run initially for a total of 15000 time steps (fullyresolved unsteady flow was achieved by this time) to achieve fully resolved unsteady structures.Then the unsteady pressure monitors were activated and the flow simulations were run for fur-ther 15000 time steps to study the spectral contents of the pressure signals at various locations

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in the cavity.

4.1 Plane Cavity, L/D = 4, W/D = 2.4

Time-mean flow

The time-mean flowfields are characterized by their mean surface static pressure coefficient(Cp) distributions. The Cp plot for this case are presented in Figure 9. Study of the meanCp distribution for this case indicates that the flow belongs to the open cavity flow type andit is found to exhibit many of the same global open cavity flow behaviours. The time-meanflow within the cavity is dominated by a large-scale recirculating flow pattern. The location ofthe centre of the large structure may be identified from the trough in the mean Cp plot that ismostly evident along the cavity floor and the structure is centred downstream of the middle ofthe cavity (approximately at x/L = 0.58). The computed Cp showed some discrepancies withthe experiment but the global characteristics are similar. Both the CFD and experimental Cpdistributions are largely flat across the floor, typical of open cavity flows. Despite the smalldifference in the Cp distributions (between CFD and experiments), the internal flow structure inthe cavity is largely in agreement to the experiment [21].

x/L

Meanpressurecoefficient

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Clean Cavity CFD

Clean Cavity Experiment

Figure 9: Centre line mean Cp along the cavity floor, L/D = 4 and W/D = 2.4.

To analyze and understand the behaviour of the mean flow inside the cavity further, a moredetailed study of the flow behaviour and structure inside the cavity using flow visualization tech-niques is necessary. Hence visualization of 2D sectional streamlines based on LIC images [24]and 3D surface flow particle tracking were used. To study 3D time-mean flow features insidethe cavity, vortex core locations were calculated and stream lines were released from the calcu-

lated cores. The resulting mean flow structure is presented in Figure 10. In addition, sectional

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streamlines of the computed time-mean velocity data are visualized using LIC in Figure 11.Figure 10 reveals the presence of two contra-rotating flow structures in the upstream third ofthe cavity which merge to a single, large recirculation further downstream. This is also evident

from the LIC image in Figure 11(g). These structures are described in ESDU Item 02008 [15]as tornado-like vortices which spiral up towards the mouth plane (i.e. the open plane) of thecavity although speculation on their subsequent movement is not given. This has been furtheranalyzed and discussed in previous works [25, 26, 27], with the aid of experiments and CFDvisualization. These structures are formed when the flow travelling upstream along the floor ofthe cavity reaches the upstream wall. The proximity of the cavity sidewall forces the flow todivert in the spanwise direction towards the centreline of the cavity. When the flow reaches thecentreline plane, it meets the flow from the other side of the centreline and is forced to turn toflow downstream but is prevented from doing so by the flow travelling upstream along the cavityfloor. The flow is forced to turn out towards the sidewall of the cavity which forms the verticaltornado-like structures seen on the cavity floor. Also visible in Figure 10 are two vortices trail-

ing downstream from the downstream corners of the cavity which is consistent with the flowvisualisation works of [28]. The meanflow structures captured by CFD in Figure 11(f-h) arealso in good agreement with the oil flow visualization of [28] (see Figure 12). Hence, the globalfeatures of the mean flowfield captured by CFD agree well with the experimental observations.The LIC images of sectional streamlines at various spanwise locations (i.e. Figures 11[a-e])also clearly indicate the three-dimensionality in the time-mean flow inside the cavity. Firstly,the most noticeable three-dimensional flow feature is the variation in the position of the core ofthe recirculating flow across the span of the cavity. Secondly, a secondary recirculating regionexists in the upstream third of the cavity for all spanwise locations except near the centreline(z/W= 0.4 and z/W= 0.5).

Time-dependent Flowfield

The unsteady flowfield was also analyzed to study the unsteady structures inside the cavity.From the result, the computed flow inside the cavity was found to be highly unsteady and dom-inated by periodic phenomena. The unsteady features inside the cavity and the shear layerfluctuation process may be seen in Figure 13 which shows the time development of tubularvortical structures in terms of the iso-surfaces of the second invariant of the velocities [29] andtheir effect on the instability of shear layer. The solid red arrow represents the flow direction andthe vertical arrow shows the direction of movement of the tubular structures. The presence oflarge-scale structures can clearly be seen from the figures. The primary effect of the 3D cavitygeometry is seen to be the introduction of a warping of the vortex axis across the span of the

cavity. This is partly due to the end walls retarding the growth of the vortical structures as theymove downstream over the cavity. Overall, the unsteady flowfield is found to dominated by thetime-dependent behaviour of the shear layer spanning the mouth of the cavity. As the incom-ing boundary layer separates at the cavity leading edge a shear layer is formed. As the shearlayer develops downstream, convective instabilities grow leading to the formation of vortex-likestructures which ultimately impinge on the downstream wall of the cavity. At the downstreamend of the cavity, the interaction of the vortical structures with the cavity trailing edge generatesdisturbances that travel upstream along the cavity floor towards the cavity leading edge. Uponreaching the leading edge of the cavity, these tubular structures trigger instabilities in the separ-ated shear layer completing the feedback loop. It is worth noting here that this event does notguarantee shear layer resonance. It all depends on the extent of the instability caused on the

shear layer. In other words, it depends on the amount of unsteady turbulent kinetic energy the

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(a) Tornado-like vortices in the cavity.

(b) View from the cavity rear wall.

Figure 10: Time-mean streamlines for 3D cavity, L/D = 4, W/D = 2.4 and M = 0.85.

tubular structures are carrying. In Figure 13, the amplification of initial instability on the shearlayer caused by the tubular structures are monitored (marked by blue ovals). The figure showsthat the shear layer instability grows quickly resulting in the violent flapping of the shear layeras it reaches the trailing edge. It will be shown later (for the same cavity geometry with verticalspoilers in the upstream boundary layer) that faintly energized structures are not able to excitestrong enough instabilities on the separated shear layer to develop resonance modes.

A more quantitative study of these variations may be obtained by analyzing the frequencycontent of the nearfield pressure time-history data using fast fourier transforms. Figure 14 showsthe comparison between experimental and computed pressure spectra. The data correspond tosampling points located at x/L = 0.90 on the floor of the cavity. From the comparison, the fre-

quency of the first resonant mode is well predicted by the computation compared to experimentalthough the CFD under-predicts the magnitude of the tone by 4dB. Mode frequency predic-tions from the modified Rossiter equation are represented by the dashed lines. The computedsecond mode frequency (1642Hz) however is lower than the experiment. The computed secondmode frequency is found to agree better with the second mode frequency predicted by the mod-ified Rossiter equation. Also CFD records the second mode as dominant whereas the reverse istrue in the experiment. These discrepancies may be due to the lack of sufficient knowledge ofexperimental test conditions that affect the cavity flowfield e.g. incoming boundary layer char-acteristics, tunnel turbulence levels, ambient density () and ambient temperature (T) (or speedof sound (a0)). Another important parameter which may have contributed to the discrepanciesis the choice of turbulence model.

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(a) Time mean streamlines in x-y plane at z/W= 0.1

(b) Time mean streamlines in x-y plane at z/W= 0.2

(c) Time mean streamlines in x-y plane at z/W= 0.3

(d) Time mean streamlines in x-y plane at z/W= 0.4

(e) Time mean streamlines in x-y plane at z/W= 0.5

(f) Upstream wall. (g) Cavity Floor. (h) Downstream wall.

Figure 11: Mean flow map for clean cavity using Line Integral Convolution, L/D = 4, W/D =2.4 and M = 0.85.

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Figure 12: Oil flow visualization for an L/D=4 cavity [[28]].

4.2 Cavity with Spoilers , L/D = 4, W/D = 2.4

Time-mean flow

The effect of spoilers on the cavity mean flowfields are investigated first by studying the meansurface static pressure coefficient (Cp) distributions and then by mean flow visualization. The Cpplot for this case are presented in Figure 15 which clearly indicates the heavy pressure loss due tothe presence of the spoiler. The mean Cp distribution is negative for the most of the cavity length,positive only after x/L = 0.93. The dissipation (at Kolmogorov scale) and self-regeneration ofturbulent kinetic energy all takes place in the boundary layer and the presence of the spoilersact as external devices that extract energy from the flow resulting in the heavy pressure loss.To demonstrate that the non-matching grid interfaces (patch grid) is effectively used withoutcreating any flow discontinuity and the flow structure is heavily dissipated, contours of meanMach number are presented in Figure 16. From the figure, it is clear that the flow is smooth

across the patch interface and there is no evidence of flow structure dissipation. To analyzeand understand the behaviour of the meanflow inside the cavity further, a more detailed studyof the flow behaviour and structure inside the cavity was performed using flow visualizationtechniques. The resulting mean flow structure is shown in Figure 17. The meanflow streamlinesdo not show any evidence of spanwise flow. Also the tornado-like vortices normally seen inempty cavities are absent. The tornado-like vortices were described as the mean flow path ofunsteady tubular structures responsible for sustaining resonance mechanisms in earlier sections.It was also highlighted (in Section 4.1) that the sustained resonant fluctuation of the shear layerwas dependant on the amount of energy the vortical structures were carrying. The dissipationof turbulent kinetic energy by the spoiler meant that the structures are weakly energized andtherefore are unable to sustain the spanwise flow. This also explains the absence of tornado-

like vortices. Also absent in Figure 17(b) are the two vortices trailing downstream from the

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(a) ta/D = 0. (b) ta/D = 1.4. (c) ta/D = 2.8.

(d) ta/D = 4.2. (e) ta/D = 5.6. (f) ta/D = 7.0.

Figure 13: Shear layer vortex evolution over one cycle of oscillation: iso-contours of the Q-criterion and vorticity sheet, L/D = 4 and W/D = 2.4; M = 0.85.

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Frequency (Hz)

Pressure

(dB)

500 1000 1500 2000 2500

120

140

0Clean cavity CFDClean cavity experiment

Figure 14: Pressure spectra at floor centreline, x/L = 0.9.

downstream corners of the cavity which is normally found in clean cavities. Instead uniformlyspaced streamwise vortices are seen to exit from the trailing wall. This also reinforces that thestatement that the flow inside the cavity is unable to sustain 3D behaviour and resonant modesdue to extraction of energy by the spoilers. This will be explained further while analyzingunsteady results. In addition, sectional streamlines of the computed time-mean velocity data arevisualized using LIC in Figure 18. The sectional streamlines at various spanwise locations (i.e.

Figures 18[b-f]) also indicate that the spanwise flow is not present. The position of the coreof the recirculating region across the span of the cavity is approximately constant including thesecondary recirculating region which exists in the upstream third of the cavity for all spanwiselocations. The main feature of the mean flow pattern in the cavity floor is also consistent withthe oil flow visualization of [21] who observed a massive separation region located in the regionofx/L = 0.25 to 0.3 where all the streamlines converge (in the CFD, streamlines are seen toconverge approximately at x/L = 0.3).

Time-dependent Flowfield

The unsteady flowfield was also analyzed to study the effect of the spoilers on the unsteady

flowfield inside the cavity. From the result, the computed flow inside the cavity was found tobe highly unsteady and dominated by periodic phenomena. The unsteady features inside thecavity and the shear layer fluctuation process may be seen in Figure 19 which shows the timedevelopment of tubular vortical structures and their effect on the instability of the shear layer.The solid red arrow represents the flow direction and the vertical arrow shows the direction ofmovement of the tubular structures. The shear layer spanning the cavity width is found to bemore stable in this case. To explain this, first the origin of spanwise fluctuations in the 3D cleancavity needs to be explained. The shear layer in clean cavities undergoes warping which is partlydue to the slowing down of the flow by the side walls. But the main reason can be described asfollows.

The wall shear stress due to the three-dimensional flat plate boundary layer upstream of the

leading edge of a 3D cavity results in a component of viscous force in the spanwise direction.

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Figure 15: Centre line mean Cp along the cavity floor, L/D = 4 and W/D = 2.4.

Figure 16: Instantaneous Mach number contours on XY-plane along the cavity centre line:Black lines represent the position of non-matching grid interfaces, L/D = 4 and W/D = 2.4.

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(a) Streamwise streamlines without tornado vortices.

(b) View from the cavity rear wall.

Figure 17: Time-mean streamlines for cavity-with-spoiler, L/D= 4, W/D= 2.4 and M= 0.85.

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(a) Time mean streamlines at side wall

(b) Time mean streamlines in x-y plane at z/W= 0.1

(c) Time mean streamlines in x-y plane at z/W= 0.2

(d) Time mean streamlines in x-y plane at z/W= 0.3

(e) Time mean streamlines in x-y plane at z/W= 0.4

(f) Time mean streamlines in x-y plane at z/W= 0.5

(g) Upstream wall. (h) Cavity Floor. (i) Downstream wall.

Figure 18: Mean flow map for cavity-with-spoiler using Line Integral Convolution, L/D = 4,W/D = 2.4 and M = 0.85.

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When the flow separates at the cavity leading edge, this spanwise force acts as an initial triggerfor the spanwise oscillation of the separated shear layer. The oscillation gets energized by thepresence of unsteady turbulent energy in the flow. In the spoiler case, however, the spoilers act

as a barrier against the spanwise instability. In addition, the loss of turbulent kinetic energy dueto the presence of a spoiler means that the shear layer instabilities do not get enough energyto amplify. This is thought to be the reason for the stable separated shear layer. The tubularstructures are seen to arrive at cavity leading edge in Figure 19 but these structures do nothave sufficient energy to cause the violent flapping of the streaks of separated shear layers.Therefore the sustained fluctuation of shear layer does not occur. In other words, the resonantmodes are absent. Frequency contents of the nearfield unsteady pressure signal was extractedusing fast fourier transforms for comparison with experiment. The resulting spectra is shownin Figure 20. From the figure, the CFD result is found to record the complete suppression ofthe dominant tones in the presence of the spoiler consistent with the experiment. The computedbroadband noise level had some discrepancies with the experiment which may be due to the

lack of sufficient knowledge of the experimental test conditions that affect the cavity flowfielde.g. incoming boundary layer characteristics, tunnel turbulence levels, ambient density ()and ambient temperature (T) (or speed of sound (a0)). In overall, computed result is found tocapture global characteristics well with compared to experiment.

(a) ta/D = 0. (b) ta/D = 1.4. (c) ta/D = 2.8.

(d) ta/D = 4.2. (e) ta/D = 5.6. (f) ta/D = 7.0.

Figure 19: Shear layer vortex evolution over one cycle of oscillation: iso-contours of the Q-

criterion and vorticity sheet, L/D = 4 and W/D = 2.4; M = 0.85.

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Frequency (Hz)

Pressure(d

B)

500 1000 1500 2000 2500

120

140Cavity with spoiler CFDCavity with spoiler experiment

Figure 20: Pressure spectra at floor centreline, x/L = 0.9.

5 Conclusion

Cavity flowfields were studied computationally at transonic speed. Mean pressure coefficientswere compared for a clean cavity against experimental data and the result showed reasonablygood agreement between the two. The experimental mean pressure coefficients for the cavitywith spoiler case was not available, however, the computed mean Cp distribution was comparedwith the clean cavity case to understand the effect of the spoiler. The result indicated thatthe presence of spoiler results in the heavy pressure loss and this is thought to be due to thedissipation of the energy at the upstream flow resulting from the presence of the spoiler.

Analysis of the unsteady flow for the first case found that the computed frequency of the first

resonant mode was in good agreement with the experiment although the CFD under-predictsthe magnitude of the tone. The computed second mode frequency is lower than the experiment,however, it is found to agree better with the second mode frequency predicted by the modifiedRossiter equation. Also CFD records the second mode as dominant whereas the reverse is truein the experiment. A strong oscillation feedback mechanism is found to be present within thecavity.

The computed unsteady result for the second case showed complete suppression of resonantmodes consistent with the experiment. In addition, both unsteady and meanflow visualizationtechniques were used to gain significant insight into the flow physics behind the tone suppres-sion. Based on the computed results a mechanism by which the spoiler suppresses the cavityresonant modes has been suggested. It is seen that the spoiler acts as an energy extracting device,

thus, dissipating the turbulent energy from the approaching boundary layer. This then reducesthe widely occurring phenomena (in empty cavities) of cross-stream warping of transverse vor-tical structures in the free shear layer. Unsteady flow within the cavity, therefore, has insufficientenergy to excite flapping of this free shear layer to cause resonance.

References

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computational investigation of cavity flow control using a passive device

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